FACTS Optimization Improves Power Loss and Voltage

Marouani Ismail et al Int. Journal of Engineering Research and Applications
ISSN : 2248-9622, Vol. 4, Issue 1( Version 1), January 2014, pp.292-299

RESEARCH ARTICLE

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OPEN ACCESS

Effect of FACTS Type to Optimization Performance and Voltage
Stability for Electrical Network
Marouani Ismail*, Allagui Brahim**, Hadj Abdallah Hsan***
*(Electrical department, College Of Technology. Jeddah. KINDGOM OF SAUDI ARABIA)
** (Electrical department, ENIS, 3038 Sfax, Tunisia)
*** (Electrical department, ENIS, 3038 Sfax, Tunisia)

ABSTRACT
In this paper, a multi objective evolutionary algorithm (MOEA) to solve optimal reactive power (VAR) dispatch
problem with flexible AC transmission system (FACTS) devices is presented. This nonlinear multi objective
problem (MOP) consists to minimize simultaneously real power loss in transmission lines and voltage deviation
at load buses, by tuning parameters and location of FACTS. The constraints of this MOP are divided to equality
constraints represented by load flow equations and inequality constraints such as, generation VAR sources and
security limits at load buses. Two types of FACTS devices, thyristor controlled series capacitor (TCSC) and
unified power flow controller (UPFC) are considered. The design problem is tested on the IEEE 30-bus system.
Keywords – Multi objective optimization; Voltage deviation; power losses; voltage stability; NSGAII; TCSC
and UPFC.

I. INTRODUCTION
The VAR dispatch problem is considered as a
MOP. It consists to determine the optimal voltage and
minimize the real power loss in transmission lines
under several equality and inequality constraints. Such
as, load flow equations and security limits. To
maintain the load buses voltage within their
permissible limits many technical methods are
proposed [1, 2]. Such as, reallocating reactive power
generation in the system adjusting transformer taps,
generator voltage and switchable VAR sources. But, to
minimize systems losses, a redistribution of reactive
power in the network can be used [2].Because their
capability to change the network parameters with a
rapid response and enhanced flexibility, FACTS
devices have taken more attention in power systems
operations as voltage profile and minimizing system
losses.
So, in first step, the objective of the present
paper is to develop a power flow model for power
system with FACTS devices. Then, a new VAR
dispatch problem is formulated. The solutions of this
problem are the FACTS parameters and location.
In the literature, several methods are used to solve a
MOP. In [3, 4], a nonlinear programming technique is
used. Other uses gradient-based optimization
algorithms by linearizing the objective function and
the system constraints around an operating point [5].
These conventional techniques consume an
important computing time and they are an iterative
methods. Also, they can be converged to a local
optimum. So, in this paper a no conventional technique
based on MOEA is used. Unlike traditional techniques,
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MOEA works on a coding of the parameters to be
optimized, rather than the parameters themselves.
Also, it employs search procedures based on the
mechanism of natural selection and survival of the
fittest. So, it can converge to the global optimum
solution. In our work, we opted to the use of the elitist
approach NSGAII (non dominated sorting genetic
algorithm) to solve the MOP.

II. FACTS DEVICES MODELS
A. Transmission line
The figure.1 shows a simple transmission line
represented by its lumped Π equivalent parameters
connected between bus-i and bus-j. The real and
reactive power flow from bus-i to bus-j can be written
as:

P  Vi 2Gij  ViV j [Gij cos( ij )  Bij sin(ij )] (1)

ij
Qij  Vi 2 ( B ij  Bsh )  ViV j [Gij sin( ij )  Bij cos( ij )]

(2)
Where

 ij   i   j . Similarly, the real and reactive

power flow from bus-j to bus-i

Pji  V j2Gij  ViVj [cos( ij )  Bij sin(ij )]

Q ji 

V j2 ( B ij  Bsh )  ViV j [Gij

(3)

sin( ij )  Bij cos( ij )]

(4)

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Yij  Gij  jBij

Bus-i

Bij 

Bus-j

V j  j

Vi  i
jB sh

2
 xc (rij2  xij  xc xij )
2
(rij2  xij )(rij2  ( xij  xc ) 2 )

Bus-i

jB sh

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Z ij  rij  jx ij

Vi  i
jB sh

Bus-j

jB sh

Figure 1. Transmission line mode
B. TCSC Model
Figure.2 shows the model of transmission line
with TCSC connected between buses i and j. The
TCSC can be considered as a static reactance  jx c .
The real and reactive power flow from bus-i to bus-j,
and from bus-j to bus-i of a line having series
impedance and a series reactance are [6]:
'
'
'
PTCSC  Vi 2Gij  ViV j [Gij cos( ij )  Bij sin(ij )]

ij
TCSC
Qij

(5)
'
'
'
 Vi 2 (Bij  Bsh )  ViVj [Gij sin(ij )  Bij cos( ij )]

(6)

TCSC
'
'
'
Pji  V j2Gij  ViV j [Gij cos( ij )  Bij sin(ij )]


(7)
'
'
'
QTCSC  Vj2 (Bij  Bsh )  ViVj [Gij sin(ij )  Bij cos( ij )]

ji
(8)
'

Where Gij

B 
'
ij

rij



r  ( xij  xc )2
 ( xij  xc )
2
ij

rij2  ( xij  xc )2

;

P

.

 Vi Gij  ViVj [Gij cosij  Bij sin ij ]
2

(9)
(10)

Q

 Vi Bij  ViV j [Gij sin ij  Bij cosij ]
2

(11)

QTCSC  V j2Bij  ViV j [Gij sin ij  Bij cosij ]
js
Where

Gij 

xc rij ( xc  2 xij )
2
(rij2  xij )(rij2  ( xij  xc )2 )

rij  jx ij

Bus-i

Bus-j

S TCSC
js

TCSC
S is

Figure 3. Injection Model of TCSC.
C. UPFC Model
The model of UPFC placed in lin-k connected
between bus-i and bus-j is shown in figure.4. UPFC
has three controllable parameters, namely, the
magnitude and the angle of inserted voltage (VT, ϕT)
and the magnitude of the current (Iq).
Based on the principle of UPFC and the vector
diagram, the basic mathematical relations can be given
as:

Arg ( IT )  Arg (Vi ) IT 

TCSC
Pjs  V j2Gij  ViV j [Gij cosij  Bij sin ij ]
TCSC
is

Figure 2. Model of TCSC.

Vi '  Vi  VT , Arg ( I q )  Arg (Vi ) 

The change in the line flow due to series
capacitance can be represented as a line without series
capacitance with power injected at the receiving and
sending ends of the line as shown in Figure.3. The real
and reactive power injections at bus-i and bus-j can be
expressed as:
TCSC
is

V j  j

 jx c

(12)
and



2

'*
T i

Re[V I ]
Vi

(13)

The power flow equations from bus-I to bus-j and from
bus-j to bus-I can be written as
*
Sij  Pij  jQij  Vi I ij  Vi ( jVi

B
 IT  I q  I i' )*
2
(14)

S ji  Pji  jQ ji  V j I *  V j ( jV j
ji

B
 I i' )*
2

(15)
The active and reactive power flow in the line
having UPFC can be written, with (13)-(15), as

PijUPFC  (Vi 2  VT2 )  2ViVT gij cos( T   i )

 V jVT [ gij cos( T   j )  bij sin(T   j )]


(16)

 ViV j ( gij cos ij  bij sin  ij )
UPFC
Pji
 V j2 gij  V jVT [ gij cos( T   j )  bij sin(T   j )]


 ViV j ( gij cos ij  bij sin  ij )

(17)

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From basic circuit theory, the injected
equivalent circuit of figure.5 can be obtained. The
injected active and reactive power at bus-i and bus-j
and reactive powers of a line having a UPFC are:
B
UPFC
Qij
 Vi I q  Vi 2 [bij  )  ViVT [(gij sin(T   j )]
2
(18)
B
 (bij  ) cos( T   i )]  ViV j ( gij sin  ij  bij cos ij )

2
B
QUPFC  V j2 (bij  )  V jVT [ gij sin(T   j )  bij cos(T   j )] (19)
ji
2
 ViV j ( gij sin  ij  bij cos  ij )
From basic circuit theory, the injected equivalent
circuit of figure.5 can be obtained. The injected active
and reactive power at bus-i and bus-j and reactive
powers of a line having a UPFC are:

PisUPFC  VT2 gij  2ViVT gij cos(T   i )  V jVT [ gij cos(T   j )
 bij sin(T   j )]

(20)

UPFC
Pjs  VjVT [ gij cos( T   j )  bij sin(T   j )] (21)


B
UPFC
Qis  Vi I q  ViVT [ gij sin(T   i )  (bij  ) cos(T   i )] (22)
2

QUPFC  VjVT [ gij sin(T   j )  bij cos( T   j )] (23)

js

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Where :
N obj : Number of objective functions.

f i : ith objective function.
The goal of a multi-objective optimization algorithm is
not only to guide the search towards the Pareto optimal
front, but, also to maintain population diversity in the
set of the nondominated solutions.
In the rest of this section, we will present the elitist
MOEA NSGAII. So, we must be start with a
presentation of the NSGA approach.
A. NSGA approach
The basic idea behind NSGA is the
ranking process executed before the selection
operation. The ranking procedure consists to find the
nondominated solutions in the current population P.
These solutions represent the first front F1. Afterwards,
this first front is eliminated from the population and
the rest is processed in the same way to identify
nondominated solutions for the second front F2. This
process continues until the population is properly
ranked. So, can write [8] :
r

P

F

j

j 1

UPFC
Bus-i
Ii

VT

I’i

Iq IT

Vi  i



rij  jx ij Bus-j

V’i
j

V j  j

B
2

j

B
2

Where, r is the number of fronts.
The same fitness value fk is assigned to all of
individuals of the same front Fk. This fitness value
decreases while passing from the front Fk to the Fk+1.
To maintain diversity in the population, a sharing
method is used. Let consider dij the variable distance
(Euclidean norm) between two solutions X i and X j .
2

(
(
 Xki )  Xk j ) 
dij 
(25)
 max

min

 Xk 
k 1  X k

Where S is the number of variables in the MOP. The
max
min
parameters X k
and X k
respectively the upper
S

Figure 4. Model of UPFC

Bus-i

Yij  gij  jbij

UPFC
S is

Bus-j

S UPFC
js

Figure 5. Injection model of UPFC.

III. MULTI-OBJECTIVE OPTIMIZATION
In a MOP, there may not exist one solution
that is best with respect to all objectives. Usually, the
aim is to determine the trade-off surface, which is a set
of nondominated solution points, known as Pareto
optimal solutions. Every individual in this set is an
acceptable solution.
For any two X 1 and X 2 , we can have one of
two possibilities : one dominates the other or none
dominates the other. In a minimization problem, we
say that the solution X 1 dominates X 2 , if the
following two conditions are satisfied [7] :
 i  1, 2 , ..., N obj , f i ( X 1 )  f i ( X 2 )

(24)

 j  1, 2 , ..., N obj , f j ( X 1 )  f j ( X 2 )





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




and lower bounds of variable X k .



(
(
(
X i  X1 i ) , X 2i ) , , X Si )



(26)

The sharing procedure is as follows :
Step 1 : Fix the niche radius  share and a small
positive number  .
Step 2 : Initiate f min  N pop   and the counter of
front j  1 .
Step 3 : From the r nondominated fronts F j which
constitute P.
r

P

F

j

j 1

Step 4 : For each individual X q  F j :


associate the dummy fitness f j( q )  f min   ;
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

calculate the niche count ncq as given in [8 ] ;



calculate the shared fitness

Step 5 :

Fmin  min(Fj'(q) ; q  Pj ) and j  j  1 .

f j'( q ) 

f j( q )
ncq

Step 6 : If j  r , then, return to step 4. Else, the
process is finished.
The MOEAs using nondominated sorting and sharing





computational complexity (M is the number of
objectives and N is the population size). Also, these
algorithms are not elitist approaches and they need to
specify the sharing parameter. To avoid these
difficulties, we present in the following an elitist
MOEA which is called Nondominated Sorting Genetic
Algorithm II (NSGAII).
B. NSGAII approach
In this approach, the sharing function
approach is replaced with a crowded comparaison.
Initially, an offspring population Qt is created from
the parent population P at the tth generation. After, a
t
combined population Rt is formed [8].

Rt  P  Qt
t
Rt is sorted into different no domination levels F j as
shown in the NSGA approach. So, we can write :
r

Rt 

F

j

, where, r is number fronts.

j 1

Finally, one iteration of the NSGAII procedure is as
follows :
Step 1 : Create the offspring population Qt from the
current population P .
t
Step 2 : Combine the two population Qt and P to
t
form Rt .
Step 3 : Find the all nondominated fronts Fi and Rt .
Step 4 : Initiate the new population P 1   and the
t
counter of front for inclusion i  1 .
Step 5 : While Pt 1  Fi  N pop , do :

P 1  P 1  Fi
t
t
i  i 1
Step 6 : Sort the last front Fi using the crowding
distance in descending order and choose the first

 N pop  Pt 1  elements of Fi .

Step 7 : Use selection, crossover and mutation
operators to create the new offspring population Qt 1
of size N obj .

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To estimate the density of solution surrounding a
particular solution X i in a nondominated set F, we
calculate the crowding distance as follows:
Step 1 : Let’s suppose q  F . For each solution X i

.

have been criticized mainly for their O MN 3

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in F, set di  0 .
Initiate m  1 .
Step 2 : Sort F in the descending order according to the
objective function of rank m.
Let’s consider I m  sort f   F  the vector of


indices, i.e.

I im

m



is the index of the solution X i in the

sorted list according to the objective function of rank
m.
Step 3 : For each solution X i which verifies
2  I im   q  1 , update the value of di as follows:
m 1

di  di 

I
f mi

m 1

I
 f mi

(27)
max
min
fm  fm
Then, the boundary solutions in the sorted list
(solutions with smallest and largest function) are
assigned an infinite distance value, i.e. if, I im  1 or
i
I m  q , di   .
Step 4 : If m  M , the procedure is finished. Else,
m   m  1 , and return to step 2.

C. Implementation of the NSGAII
The proposed NSGAII has been implemented
using real-coded genetic algorithm (RCGA)[7]. So, a
chromosome X corresponding to a decision variable is
represented as a string of real values xi , i.e.

X  x1 x2 ...xlchrom . lchrom is the chromosome size
and xi is a real number within its lower limit ai and
upper limit bi . i.e. xi   ai ,bi  . Thus, for two
individuals having as chromosomes respectively X
and Y and after generating a random number
   0,1 , the crossover operator can provide two
chromosomes X ' and Y' with a probability PC as
follows [8] :

X '   X  1    Y

(28)

Y '  1    X  Y

In this study, the non-uniform mutation
operator has been employed. So, at the tth generation,
a parameter xi of the chromosome X will be
'
transformed to other parameter xi with a probability

Pm as follows :

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 xi    t,bi  xi  , if

xi'  
 xi    t,xi  ai  , if




  t, y   y 1  r 

1t / gmax 





 0
 1

(29)

(30)

Where  is random binary number, r is a random
number r   0 ,1 and g max is the maximum number
of generations. 
arbitrarily.

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Vi ref is usually set to be 1.0 pu.
C. Problem constraints
 Equality constraints
These constraints represent typical load flow equations
as follows :

PGi  PDi 

N

V G cos      B sin      0
j

ij

i

j

ij

i

j

(33)

j 1

is a positive constant chosen
QGi  QDi 

N

V G sin      B cos      0


j

ij

i

j

ij

i

j

(34)

j 1

IV. PROBLEM FORMULATION
A. Problem formulation
The optimal VAR dispatch problem is to
optimise the steady performance of a power system in
terms of one or more objective functions while
satisfying several equality and inequality constraints.
In this section, we suppose that the extremities FACTS
devices are referred by bus i and j.
B. Objective functions
 Real power loss
This objective consists to minimise the real
power loss PL in transmission lines that can be
expressed as [ 1 ] :

PL 

Nb

P

k

k 1

Where :
PGi and QGi : generator real and reactive power at i-th
bus, respectively;
PDi and QDi : load real and reactive power at i-th
bus, respectively;
Gij and Bij : transfer conductance and susceptance
between buses i and j, respectively.
 Inequality constraints
These constraints represent are :
a)
Voltage stability limits
The voltage collapse point or critical point
(VCP) shown in Figure 6, is defined by the maximum
power transfer to a load at bus i without violating
voltage stability limits. VCP at the load bus i must be
less than or equal to one.

Where :



 Pi,SSSC or Pi,UPFC if k  i

(31)
Pk   Pj ,SSSC or Pj ,UPFC if k  j
 Nb
 V V Y cos      ,if k  i, j
 k h kh 
k h kh

 h1
N b : number of buses;
Vk  k and Vh  h : respectively voltages at bus k



and h;
Ykh and  kh : respectively modulus and argument of
the kh-th element of the nodal admittance matrix Y .
 Voltage deviation
This objective is to minimize the deviation in voltage
magnitude at load buses that can be expressed as :

VD 

NL

 V V
i

ref

i

(32)

i 1

Where :
N L : number of load buses;

Vi ref : prespecified reference value of the voltage
magnitude at the i-th load bus.

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VCP  1

Figure 6. Power-Voltage Curve

(35)
b)
Security constraints
These include the constraints of voltage at load buses
VL as follows:
min
max
VLi  VLi  VLi , i  1,,..., N L

(36)

c)
FACTS devices constraints :
The FACTS devices limit is given by:

 0.5 X L  xc  0.5 X L

(37)

200MVAR  QUPFC  200 MVAR

(38)

Where :
XL : Original line reactance in (pu).
xc : Reactance added to the line where TCSC is placed
in (pu)
QUPFC : reactance power injected at UPFC placed in
MVAR.
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(32)


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V. IEEE 30-BUS TEST SYSTEM
Figure 7 shows the IEEE 30-bus system
which consists of 6 generator buses, 24 load buses and
41 transmission lines of which 4 branches (6–9), (6–
10), (4–12), and (28–27) are with the tap setting
transformer. The transmission line parameters of this
system and the base loads are taken from [9]. For the
RPD problem, the candidate buses for reactive power
compensation are 10, 12, 15, 17, 20, 21, 23, 24, and
29. The lower voltage magnitude limits at all buses are
0.95 p.u. and the upper limits are 1.1 for all the PV
buses and 1.05 p.u. for all the PQ buses. The lower and
upper limits of the transformer in tappings are 0.9 and
1.1 p.u. respectively. Considering a base power of 100
MVA for the overall system and base voltages of 100
KV.

Figure 8 : Convergence of voltage deviation objective
with FACTS devices.
In the figure.9, the red curve indicates the
effect of the UPFC, the blue curve illustrates the effect
of the TCSC. we can say that the UPFC has the most
significant effect compared to TCSC.

Figure: 7 IEEE 30 bus systems
In this work, four branches, (6, 10),(4, 12),
(10, 22) and (28, 27) are installed with UPFC and three
branches, (1, 3), (3, 4) and (2, 5) are installed with
TCSC.The best location of FACTS devices for the
optimal case is the branche (10,22) for UPFC and the
branche (2,5) for the TCSC.
Figure 8 and 9 shows the convergence of the
voltage deviation and power loss respectively to 0.172
pu and 4.447MW with UPFC, and 0.183 pu and 4.512
MW with TCSC.

Figure 9 : Convergence of power loss objective with
FACTS devices
The diversity of the pareto optimal set over
the trade off surface is shown in figure 10.

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According to Figure 11, we see very well that
the bus 29 is the load bus that has the largest voltage
variation, because it is very far from the generator
buses. Figure 12 shows the effect of UPFC in
improving the stability of the latter power.

VI. CONCLUSION

Figure 10:Pareto-optimal front of the proposed
approach
Figure 11 provides voltage magnitude of all
buses obtained from TCSC and UPFC.
1.12
1.1
UPFC
TCSC
Uper limit
Lower limit

1.08

Voltage [pu]

1.06
1.04
1.02
1

This paper presents the application of
NSGAII technique to find the optimal location of
FACTS devices for minimizing simultaneously real
power loss in transmission lines and voltage deviation
in order to obtained the better voltage stability at load
buses, under several equality and inequality
constraints. An existing Newton-Raphson algorithm is
modified to include FACTS devices is used to solve
load flow equations.
The FACTS devices can provide control of
voltage magnitude, voltage phase angle and
impedance. Therefore, it can be utilized to effectively
increase power transfer capability of the existing
power transmission lines, since it reduces considerably
the real power losses. The NSGAII achieves better
solution for the voltage stability with UPFC than
TCSC fixed at the given locations.
The simulations results obtained for the
IEEE-30 bus network showed the effectiveness of the
proposed method. This approach is able to give several
possible solutions simultaneously. These solutions are
presented by Pareto-optimal front. Also, this method
does not impose any limitation on the number of
objectives, constraints.

0.98

REFERENCES
0.96
0.94

[1]
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Bus number

Figure 11 : Voltage profile with TCSC and UPFC
[2]
1.025
With UPFC
Without UPFC

1.02

[3]

Voltage magnitude [pu]

1.015
1.01
1.005

[4]

1
0.995

[5]

0.99
0.985
0.98

[6]
1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

Total active load [pu]

3

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Electr Power Syst Res 2003;65(1):71-81..
Verma K.S., Singh S.N., Gupta H.O.,
2001.FACTS
devices location for
enhancement of total transfer capability,

Figure 12.P-V curves at load bus 29
www.ijera.com

298 | P a g e


[7]

[8]

[9]

www.ijera.com

Power Engineering Society Winter Meeting,
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299 | P a g e

FACTS Optimization Improves Power Loss and Voltage

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